Compound Interest Formula Explained

The math behind compound interest is simpler than it looks. Here's everything you need.

The basic compound interest formula

FV = P × (1 + r/n)^n×t

FV = Future value
P = Principal (initial investment)
r = Annual interest rate (decimal, so 7% = 0.07)
n = Number of compounding periods per year (12 for monthly, 1 for annual)
t = Number of years

Worked example

Invest $10,000 at 7% compounded monthly for 20 years:

FV = 10,000 × (1 + 0.07/12)^12×20 = 10,000 × (1.00583)²⁴⁰ ≈ $40,387

With monthly contributions (annuity formula)

When you also contribute regularly, you need a second formula — the future value of an annuity:

FV = PMT × [((1 + r/n)^n×t − 1) / (r/n)]

PMT = Periodic contribution (e.g. $500/month)

Worked example

Contribute $500/month at 7% compounded monthly for 20 years:

FV = 500 × [((1.00583)²⁴⁰ − 1) / 0.00583] ≈ $260,463

Combining both

When you start with a lump sum and contribute monthly, simply add the two formulas together. With $10,000 initial + $500/month at 7% for 20 years: ≈ $300,850.

The Rule of 72

A handy shortcut: divide 72 by your interest rate to estimate how long it takes to double your money.

At 6%: 72 / 6 = 12 years
At 8%: 72 / 8 = 9 years
At 12%: 72 / 12 = 6 years

Want to skip the math? Use the compound interest calculator and let it crunch the numbers for you.